Exploring the connections between exact coherent structures and attractors in active nematic channel flow

Exact Coherent Structures (ECS) are stationary, periodic, quasiperiodic, or traveling wave solutions of the governing equations that, together with their invariant manifolds, serve as an organizing template of the dynamics of a fluid system. Active nematics is a class of active fluids that exhibits rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. In this work, we compute over 100 ECSs in a 2D active nematic channel flow system, and provide evidence that these ECSs are shadowed by typical trajectories of the system. We also discuss the presence of robust heteroclinic cycles in the system that cycle between the two opposite flowing unidirectional flow states, as well as several other exotic trajectories that can be explained using the ECS framework.